# Singular Lagrangians and precontact Hamiltonian Systems

## TL;DR

This paper explores singular Lagrangian systems within contact geometry, developing a constraint algorithm, a Hamiltonian counterpart, and a Dirac-Jacobi bracket, highlighting dissipative behaviors absent in symplectic frameworks.

## Contribution

It introduces a novel constraint algorithm for singular Lagrangian systems in contact geometry and establishes their Hamiltonian equivalence, extending geometric methods to dissipative systems.

## Key findings

- Developed a contact geometric constraint algorithm
- Constructed a Hamiltonian formulation for singular systems
- Established the equivalence between Lagrangian and Hamiltonian formalisms

## Abstract

In this paper we discuss singular Lagrangian systems on the framework of contact geometry. These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic one studied by Gotay and Nester (the geometrization of the well-known Dirac-Bergman algorithm). We also construct the Hamiltonian counterpart and prove the equivalence with the Lagrangian side. A Dirac-Jacobi bracket is constructed similar to the Dirac bracket.